Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\sqrt{e^{x \cdot x - 1}} \cdot \sqrt{e^{x \cdot x - 1}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\sqrt{e^{x \cdot x - 1}} \cdot \sqrt{e^{x \cdot x - 1}}
double f(double x) {
        double r34829 = 1.0;
        double r34830 = x;
        double r34831 = r34830 * r34830;
        double r34832 = r34829 - r34831;
        double r34833 = -r34832;
        double r34834 = exp(r34833);
        return r34834;
}
↓
double f(double x) {
        double r34835 = x;
        double r34836 = r34835 * r34835;
        double r34837 = 1.0;
        double r34838 = r34836 - r34837;
        double r34839 = exp(r34838);
        double r34840 = sqrt(r34839);
        double r34841 = r34840 * r34840;
        return r34841;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{x \cdot x - 1}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{e^{x \cdot x - 1}} \cdot \sqrt{e^{x \cdot x - 1}}}\]

  5. Final simplification0.0

    \[\leadsto \sqrt{e^{x \cdot x - 1}} \cdot \sqrt{e^{x \cdot x - 1}}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))